Validation of Multiple Imputation in SPHC-B 2010

Notes: This document summarizes only the key outputs of the final multiple imputation process for SPHC-B 2010. More detailed R scripts are available in the R Notebook “SPHC-B-2010.Rmd”.

1. Load Packages

library(naniar)
library(dplyr)
library(jomo)
library(mitml)
library(ggplot2)

2. SPHC-B 2010

2.1. Incomplete dataset

load("/Volumes/LGBT Project data/Multiple Imputation/d_2010_incomplete.RData")
summary( d_2010_incomplete )

    sampling_strata_region calibrated_weight no.of.population   sexual_identity_2010 sexual_identity_fluidity
 Lidingö       : 1368      Min.   :  5.424   Min.   :  6831   Heterosexual:28471     0   :11534              
 Nacka         : 1342      1st Qu.: 25.180   1st Qu.: 26849   Homosexual  :  361     1   : 1656              
 Nynäshamn     : 1284      Median : 43.971   Median : 34342   Bisexual    :  381     NA's:17577              
 Upplands-Väsby: 1268      Mean   : 52.157   Mean   : 41143   Uncertain   :  394                             
 Sundbyberg    : 1144      3rd Qu.: 70.027   3rd Qu.: 56341   NA's        : 1160                             
 Botkyrka      : 1082      Max.   :282.667   Max.   :101916                                                  
 (Other)       :23279                                                                                        
      age             sex              country_of_birth       education         income                 marital_status 
 Min.   : 18.00   Male  :13829   Sweden        :25157   <=9 years  : 4998   Min.   :     0   Never married    : 9887  
 1st Qu.: 37.00   Female:16938   Europe        : 3343   10-12 years:12548   1st Qu.:  1917   Currently married:15066  
 Median : 51.00                  Outside Europe: 2267   >=13 years :13001   Median :  2696   Other            : 5814  
 Mean   : 51.04                                         NA's       :  220   Mean   :  3247                            
 3rd Qu.: 65.00                                                             3rd Qu.:  3667                            
 Max.   :104.00                                                             Max.   :450719                            
                                                                                                                      
 living_alone personal_support weight_strata  
 yes : 6432   yes :26882       2      : 1238  
 no  :24005   no  : 3474       16     : 1235  
 NA's:  330   NA's:  411       8      : 1232  
                               11     : 1232  
                               14     : 1232  
                               18     : 1232  
                               (Other):23366

sapply( d_2010_incomplete, class ) # all continuous variables are numeric, and all categorical variables are factor

  sampling_strata_region        calibrated_weight         no.of.population     sexual_identity_2010 
                "factor"                "numeric"                "numeric"                 "factor" 
sexual_identity_fluidity                      age                      sex         country_of_birth 
                "factor"                "numeric"                 "factor"                 "factor" 
               education                   income           marital_status             living_alone 
                "factor"                "numeric"                 "factor"                 "factor" 
        personal_support            weight_strata 
                "factor"                 "factor"

miss_var_summary( d_2010_incomplete ) # 57.1% missing in sexual_identity_fluidity, 3.8% in sexual_identity_2010, 1.3% in personal_support, 1.1% in living_alone, and 0.7% in education

2.2. Two-level multivariate normal imputation

# specify imputation model
# fml_imp_2010 <- sexual_identity_fluidity + sexual_identity_2010 + personal_support + living_alone + education ~ 1 + age*sex + country_of_birth + income + marital_status + ( 1 | weight_strata )

# final imputation with the chosen number of iterations
# imp_final_2010 <- jomoImpute( data = d_2010_incomplete,
#                               formula = fml_imp_2010,
#                               random.L1 = "full",
#                               n.burn = 2000,
#                               n.iter = 1000,
#                               m = 80,
#                               seed = 12345
#                               ) # took around 20 hours

load("/Volumes/LGBT Project data/Multiple Imputation/imp_final_2010.RData")
summary( imp_final_2010 ) # summarize model and display convergence statistics


Call:

jomoImpute(data = d_2010_incomplete, formula = fml_imp_2010, 
    random.L1 = "full", n.burn = 2000, n.iter = 1000, m = 80, 
    seed = 12345)

Cluster variable:         weight_strata 
Target variables:         sexual_identity_fluidity sexual_identity_2010 personal_support living_alone education 
Fixed effect predictors:  (Intercept) age sex country_of_birth income marital_status age:sex 
Random effect predictors: (Intercept) 

Performed 2000 burn-in iterations, and generated 80 imputed data sets,
each 1000 iterations apart. 

Potential scale reduction (Rhat, imputation phase):
 
         Min   25%  Mean Median   75%   Max
Beta:  1.000 1.000 1.004  1.001 1.004 1.028
Psi:   1.000 1.000 1.000  1.000 1.000 1.001
Sigma: 1.000 1.000 1.073  1.012 1.056 1.989

Largest potential scale reduction:
Beta: [1,2], Psi: [2,1], Sigma: [42,1]

Missing data per variable:
    weight_strata sexual_identity_fluidity sexual_identity_2010 personal_support living_alone education
MD% 0             57.1                     3.8                  1.3              1.1          0.7      
    sampling_strata_region calibrated_weight no.of.population age sex country_of_birth income marital_status
MD% 0                      0                 0                0   0   0                0      0

plot( imp_final_2010, trace = "all", print = "beta" ) # check trace and autocorrelation plots

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2.3. Validate imputed data

# extract imputed datasets
original_data_2010 <- mitmlComplete( imp_final_2010, print = 0 ) # extract original incomplete dataset
implist_2010 <- mitmlComplete( imp_final_2010, print = "all" ) # extract all imputed datasets

original_data_2010$imputation <- "0"
all_data_2010 <- bind_rows( original_data_2010,
                            bind_rows( implist_2010, .id = "imputation" ) ) # merge datasets
all_data_2010$imputation <- as.numeric( all_data_2010$imputation )
summary( all_data_2010 )

 weight_strata     sexual_identity_fluidity   sexual_identity_2010 personal_support living_alone         education      
 2      : 100278   0   :2112580             Heterosexual:2391929   yes :2205638     yes : 529530   <=9 years  : 409994  
 16     : 100035   1   : 361970             Homosexual  :  30755   no  : 286078     no  :1962267   10-12 years:1023200  
 8      :  99792   NA's:  17577             Bisexual    :  32530   NA's:    411     NA's:    330   >=13 years :1058713  
 11     :  99792                            Uncertain   :  35753                                   NA's       :    220  
 14     :  99792                            NA's        :   1160                                                        
 18     :  99792                                                                                                        
 (Other):1892646                                                                                                        
    sampling_strata_region calibrated_weight no.of.population      age             sex                country_of_birth  
 Lidingö       : 110808    Min.   :  5.424   Min.   :  6831   Min.   : 18.00   Male  :1120149   Sweden        :2037717  
 Nacka         : 108702    1st Qu.: 25.180   1st Qu.: 26849   1st Qu.: 37.00   Female:1371978   Europe        : 270783  
 Nynäshamn     : 104004    Median : 43.971   Median : 34342   Median : 51.00                    Outside Europe: 183627  
 Upplands-Väsby: 102708    Mean   : 52.157   Mean   : 41143   Mean   : 51.04                                            
 Sundbyberg    :  92664    3rd Qu.: 70.027   3rd Qu.: 56341   3rd Qu.: 65.00                                            
 Botkyrka      :  87642    Max.   :282.667   Max.   :101916   Max.   :104.00                                            
 (Other)       :1885599                                                                                                 
     income                 marital_status      imputation
 Min.   :     0   Never married    : 800847   Min.   : 0  
 1st Qu.:  1917   Currently married:1220346   1st Qu.:20  
 Median :  2696   Other            : 470934   Median :40  
 Mean   :  3247                               Mean   :40  
 3rd Qu.:  3667                               3rd Qu.:60  
 Max.   :450719                               Max.   :80

# sexual identity in 2010
ggplot( all_data_2010[ !is.na( all_data_2010$sexual_identity_2010 ), ],
        aes( fill = sexual_identity_2010, x = imputation ) ) + 
  geom_bar( position = "fill" ) + 
  scale_y_continuous( labels = scales::percent ) + 
  scale_fill_discrete( name = "Sexual identity in 2010" ) +
  labs(
    x = "Imputation number",
    y = "Proportion",
    caption = "Notes: Imputation number 0 represents the original incomplete dataset." ) +
  theme_classic() +
  theme( axis.title.x = element_text( family = "Arial", size = 11 ),
         axis.text.x = element_text( family = "Arial", size = 11 ),
         axis.text.y = element_text( family = "Arial", size = 11 ),
         axis.title.y = element_text( family = "Arial", size = 11 ),
         legend.text = element_text( family = "Arial", size = 10 ),
         legend.title = element_text( family = "Arial", size = 10 ),
         legend.position = "bottom",
         plot.caption = element_text( family = "Arial", size = 10, hjust = 0 ) 
  )


# change in sexual identity during 2010-2021
ggplot( all_data_2010[ !is.na( all_data_2010$sexual_identity_fluidity ), ],
        aes( fill = sexual_identity_fluidity, x = imputation ) ) + 
  geom_bar( position = "fill" ) + 
  scale_y_continuous( labels = scales::percent ) + 
  scale_fill_discrete( name = "Change in sexual identity during 2010-2021", labels = c( "No", "Yes" ) ) +
  labs(
    x = "Imputation number",
    y = "Proportion",
    caption = "Notes: Imputation number 0 represents the original incomplete dataset." ) +
  theme_classic() +
  theme( axis.title.x = element_text( family = "Arial", size = 11 ),
         axis.text.x = element_text( family = "Arial", size = 11 ),
         axis.text.y = element_text( family = "Arial", size = 11 ),
         axis.title.y = element_text( family = "Arial", size = 11 ),
         legend.text = element_text( family = "Arial", size = 10 ),
         legend.title = element_text( family = "Arial", size = 10 ),
         legend.position = "bottom",
         plot.caption = element_text( family = "Arial", size = 10, hjust = 0 ) 
  )


# education
ggplot( all_data_2010[ !is.na( all_data_2010$education ), ],
        aes( fill = education, x = imputation ) ) + 
  geom_bar( position = "fill" ) + 
  scale_y_continuous( labels = scales::percent ) + 
  scale_fill_discrete( name = "Level of education" ) +
  labs(
    x = "Imputation number",
    y = "Proportion",
    caption = "Notes: Imputation number 0 represents the original incomplete dataset." ) +
  theme_classic() +
  theme( axis.title.x = element_text( family = "Arial", size = 11 ),
         axis.text.x = element_text( family = "Arial", size = 11 ),
         axis.text.y = element_text( family = "Arial", size = 11 ),
         axis.title.y = element_text( family = "Arial", size = 11 ),
         legend.text = element_text( family = "Arial", size = 10 ),
         legend.title = element_text( family = "Arial", size = 10 ),
         legend.position = "bottom",
         plot.caption = element_text( family = "Arial", size = 10, hjust = 0 ) 
  )


# living status
ggplot( all_data_2010[ !is.na( all_data_2010$living_alone ), ],
        aes( fill = living_alone, x = imputation ) ) + 
  geom_bar( position = "fill" ) + 
  scale_y_continuous( labels = scales::percent ) + 
  scale_fill_discrete( name = "Living alone", labels = c( "Yes", "No" ) ) +
  labs(
    x = "Imputation number",
    y = "Proportion",
    caption = "Notes: Imputation number 0 represents the original incomplete dataset." ) +
  theme_classic() +
  theme( axis.title.x = element_text( family = "Arial", size = 11 ),
         axis.text.x = element_text( family = "Arial", size = 11 ),
         axis.text.y = element_text( family = "Arial", size = 11 ),
         axis.title.y = element_text( family = "Arial", size = 11 ),
         legend.text = element_text( family = "Arial", size = 10 ),
         legend.title = element_text( family = "Arial", size = 10 ),
         legend.position = "bottom",
         plot.caption = element_text( family = "Arial", size = 10, hjust = 0 ) 
  )


# personal support
ggplot( all_data_2010[ !is.na( all_data_2010$personal_support ), ],
        aes( fill = personal_support, x = imputation ) ) + 
  geom_bar( position = "fill" ) + 
  scale_y_continuous( labels = scales::percent ) + 
  scale_fill_discrete( name = "Personal support", labels = c( "Yes", "No" ) ) +
  labs(
    x = "Imputation number",
    y = "Proportion",
    caption = "Notes: Imputation number 0 represents the original incomplete dataset." ) +
  theme_classic() +
  theme( axis.title.x = element_text( family = "Arial", size = 11 ),
         axis.text.x = element_text( family = "Arial", size = 11 ),
         axis.text.y = element_text( family = "Arial", size = 11 ),
         axis.title.y = element_text( family = "Arial", size = 11 ),
         legend.text = element_text( family = "Arial", size = 10 ),
         legend.title = element_text( family = "Arial", size = 10 ),
         legend.position = "bottom",
         plot.caption = element_text( family = "Arial", size = 10, hjust = 0 ) 
  )

---
title: "Validation of Multiple Imputation in SPHC-B 2010"
author: Willi Zhang (willi.zhang@ki.se), Matteo Quartagno
output: html_notebook
editor_options:
  chunk_output_type: inline
---

<br>

##### *Notes:* This document summarizes only the key outputs of the final multiple imputation process for SPHC-B 2010. More detailed R scripts are available in the R Notebook ["SPHC-B-2010.Rmd"](https://github.com/willizhang/Temporal-Trends-in-Sexual-Identity-and-Sociodemographic-Disparities-in-Stockholm-County-2010-to-2021/blob/main/SPHC-B-2010.Rmd).

<br>

### 1. Load Packages
```{r echo=TRUE, message=FALSE, warning=FALSE}
library(naniar)
library(dplyr)
library(jomo)
library(mitml)
library(ggplot2)
```

### 2. SPHC-B 2010
#### 2.1. Incomplete dataset
```{r}
load("/Volumes/LGBT Project data/Multiple Imputation/d_2010_incomplete.RData")
summary( d_2010_incomplete )
sapply( d_2010_incomplete, class ) # all continuous variables are numeric, and all categorical variables are factor
miss_var_summary( d_2010_incomplete ) # 57.1% missing in sexual_identity_fluidity, 3.8% in sexual_identity_2010, 1.3% in personal_support, 1.1% in living_alone, and 0.7% in education
```

#### 2.2. Two-level multivariate normal imputation
```{r}
# specify imputation model
# fml_imp_2010 <- sexual_identity_fluidity + sexual_identity_2010 + personal_support + living_alone + education ~ 1 + age*sex + country_of_birth + income + marital_status + ( 1 | weight_strata )

# final imputation with the chosen number of iterations
# imp_final_2010 <- jomoImpute( data = d_2010_incomplete,
#                               formula = fml_imp_2010,
#                               random.L1 = "full",
#                               n.burn = 2000,
#                               n.iter = 1000,
#                               m = 80,
#                               seed = 12345
#                               ) # took around 20 hours

load("/Volumes/LGBT Project data/Multiple Imputation/imp_final_2010.RData")
summary( imp_final_2010 ) # summarize model and display convergence statistics
plot( imp_final_2010, trace = "all", print = "beta" ) # check trace and autocorrelation plots
```

#### 2.3. Validate imputed data
```{r}
# extract imputed datasets
original_data_2010 <- mitmlComplete( imp_final_2010, print = 0 ) # extract original incomplete dataset
implist_2010 <- mitmlComplete( imp_final_2010, print = "all" ) # extract all imputed datasets

original_data_2010$imputation <- "0"
all_data_2010 <- bind_rows( original_data_2010,
                            bind_rows( implist_2010, .id = "imputation" ) ) # merge datasets
all_data_2010$imputation <- as.numeric( all_data_2010$imputation )
summary( all_data_2010 )

# sexual identity in 2010
ggplot( all_data_2010[ !is.na( all_data_2010$sexual_identity_2010 ), ],
        aes( fill = sexual_identity_2010, x = imputation ) ) + 
  geom_bar( position = "fill" ) + 
  scale_y_continuous( labels = scales::percent ) + 
  scale_fill_discrete( name = "Sexual identity in 2010" ) +
  labs(
    x = "Imputation number",
    y = "Proportion",
    caption = "Notes: Imputation number 0 represents the original incomplete dataset." ) +
  theme_classic() +
  theme( axis.title.x = element_text( family = "Arial", size = 11 ),
         axis.text.x = element_text( family = "Arial", size = 11 ),
         axis.text.y = element_text( family = "Arial", size = 11 ),
         axis.title.y = element_text( family = "Arial", size = 11 ),
         legend.text = element_text( family = "Arial", size = 10 ),
         legend.title = element_text( family = "Arial", size = 10 ),
         legend.position = "bottom",
         plot.caption = element_text( family = "Arial", size = 10, hjust = 0 ) 
  )

# change in sexual identity during 2010-2021
ggplot( all_data_2010[ !is.na( all_data_2010$sexual_identity_fluidity ), ],
        aes( fill = sexual_identity_fluidity, x = imputation ) ) + 
  geom_bar( position = "fill" ) + 
  scale_y_continuous( labels = scales::percent ) + 
  scale_fill_discrete( name = "Change in sexual identity during 2010-2021", labels = c( "No", "Yes" ) ) +
  labs(
    x = "Imputation number",
    y = "Proportion",
    caption = "Notes: Imputation number 0 represents the original incomplete dataset." ) +
  theme_classic() +
  theme( axis.title.x = element_text( family = "Arial", size = 11 ),
         axis.text.x = element_text( family = "Arial", size = 11 ),
         axis.text.y = element_text( family = "Arial", size = 11 ),
         axis.title.y = element_text( family = "Arial", size = 11 ),
         legend.text = element_text( family = "Arial", size = 10 ),
         legend.title = element_text( family = "Arial", size = 10 ),
         legend.position = "bottom",
         plot.caption = element_text( family = "Arial", size = 10, hjust = 0 ) 
  )

# education
ggplot( all_data_2010[ !is.na( all_data_2010$education ), ],
        aes( fill = education, x = imputation ) ) + 
  geom_bar( position = "fill" ) + 
  scale_y_continuous( labels = scales::percent ) + 
  scale_fill_discrete( name = "Level of education" ) +
  labs(
    x = "Imputation number",
    y = "Proportion",
    caption = "Notes: Imputation number 0 represents the original incomplete dataset." ) +
  theme_classic() +
  theme( axis.title.x = element_text( family = "Arial", size = 11 ),
         axis.text.x = element_text( family = "Arial", size = 11 ),
         axis.text.y = element_text( family = "Arial", size = 11 ),
         axis.title.y = element_text( family = "Arial", size = 11 ),
         legend.text = element_text( family = "Arial", size = 10 ),
         legend.title = element_text( family = "Arial", size = 10 ),
         legend.position = "bottom",
         plot.caption = element_text( family = "Arial", size = 10, hjust = 0 ) 
  )

# living status
ggplot( all_data_2010[ !is.na( all_data_2010$living_alone ), ],
        aes( fill = living_alone, x = imputation ) ) + 
  geom_bar( position = "fill" ) + 
  scale_y_continuous( labels = scales::percent ) + 
  scale_fill_discrete( name = "Living alone", labels = c( "Yes", "No" ) ) +
  labs(
    x = "Imputation number",
    y = "Proportion",
    caption = "Notes: Imputation number 0 represents the original incomplete dataset." ) +
  theme_classic() +
  theme( axis.title.x = element_text( family = "Arial", size = 11 ),
         axis.text.x = element_text( family = "Arial", size = 11 ),
         axis.text.y = element_text( family = "Arial", size = 11 ),
         axis.title.y = element_text( family = "Arial", size = 11 ),
         legend.text = element_text( family = "Arial", size = 10 ),
         legend.title = element_text( family = "Arial", size = 10 ),
         legend.position = "bottom",
         plot.caption = element_text( family = "Arial", size = 10, hjust = 0 ) 
  )

# personal support
ggplot( all_data_2010[ !is.na( all_data_2010$personal_support ), ],
        aes( fill = personal_support, x = imputation ) ) + 
  geom_bar( position = "fill" ) + 
  scale_y_continuous( labels = scales::percent ) + 
  scale_fill_discrete( name = "Personal support", labels = c( "Yes", "No" ) ) +
  labs(
    x = "Imputation number",
    y = "Proportion",
    caption = "Notes: Imputation number 0 represents the original incomplete dataset." ) +
  theme_classic() +
  theme( axis.title.x = element_text( family = "Arial", size = 11 ),
         axis.text.x = element_text( family = "Arial", size = 11 ),
         axis.text.y = element_text( family = "Arial", size = 11 ),
         axis.title.y = element_text( family = "Arial", size = 11 ),
         legend.text = element_text( family = "Arial", size = 10 ),
         legend.title = element_text( family = "Arial", size = 10 ),
         legend.position = "bottom",
         plot.caption = element_text( family = "Arial", size = 10, hjust = 0 ) 
  )
```